Frege said very little about modality. Section 4 of his first book, Begriffsschrift (Frege Reference Frege1879), contains all of it. It takes, in my view, little discernment to notice that this Section 4 is a commentary on Section 9 of a certain Kritik der reinen Vernunft. Indeed, Frege follows the order in which Kant discusses the players at the Urteilstafel, ending with the modalities of judgment. When Frege gets there, he uses some words that one might hear as harsh. Calling a Satz necessary, for instance, “has no meaning for us,” since doing so has nothing to do with the beurteilbare Inhalt expressed, nothing to do with what is of significance for logic. Presenting a Satz as possible has no more to do with judgeable content expressed. Both give a Wink (if not a nod), in the former case about a speaker’s grounds for judgment, and in the latter, either about why she does not really judge at all, or that he is really judging (what we would call) an existential generalization.
Having thus exorcised modality, Frege never, through the heydays of Grundlagen and Grundgesetze volume I, the tottering of arithmetic at the hands of Russell, to the last meditations on logic, mentions it again. I take it that this is not (merely) because of lack of interest, or the Weltanschauung. Rather, as Frege’s philosophy evolved, he came to commitments that preclude taking modality to be logically or philosophically fundamental. Someone who takes Frege to be a great philosopher, on the same level as, say, David Lewis, might be shocked, perhaps offended, by my story of why Frege rejects modality, and to express that distaste by some term of opprobrium, such as “structural history.” Charles, as we know from Frege: The Pure Business of Being True (Travis, Reference Travis2021, hereafter FPB), takes Frege to be a great philosopher, but on the same level as Kant. Perhaps to spare my feelings, he has, graciously, declined (so far) to call my tale structural history. Instead, he asked me, “Is Frege really opposed to modality?” What follows here is an answer of sorts. Since the symposium is on Charles’s book, I will not go very much into my grounds for answering yes. Rather, I will think a bit about whether Charles’s Frege has to embrace some conception of modality. Just in case you are itching to get to some other paper, I will let out the spoiler: no. There are, prima facie, two ways in which modality seems to find a foothold in the pure business of being true: the relativization of truth to occasion or understanding, and the nature of representation through concepts. Appearances are deceiving: neither establish modality as required in that pure business. But I would like also to say that I would not be crestfallen were the answer to turn out, on further investigation, to be yes. For I am not quite done with the structural history business: in a sequel to the one about Frege (and Russell before 1919 or so) I aim to make out that early Wittgenstein came to see possibility as intrinsic to Fregean Gedanken.
One last note before beginning. I will venture beyond FPB, and make use of Charles’s previous discussions of Frege, in Occasion-Sensitivity (Travis, Reference Travis2008, hereafter OS), Objectivity and the Parochial (Travis, Reference Travis2010, hereafter OP), and Perception (Travis, Reference Travis2013, hereafter PEF).
1. Shake Hands Forever
A particularly intriguing aspect of Charles’s reading of Frege is his view that Frege’s notion of thought, Gedanke, is compatible with the notions of occasion-sensitivity (OS, unitalicized, hereafter) Charles takes from Austin and the later Wittgenstein.
Here’s how he presents the “core idea of [OS]”:
When I say the sky to be blue, I speak of the sky, express the concept of being blue, and represent the sky as what that concept is a concept of. For all of which I may have said any of many things, each different from the others in when it would be true. [C]oncepts admit of many applications, and are satisfied (or not) only on one such or another.
There are many understandings of being what the concept is of being; there are, correspondingly, many understandings of satisfying the concept. (OS, 3; emphases mine)
This has a well-known upshot for semantics: the meanings of non-indexical, non-demonstrative expressions such as “blue” under-determine the conditions for truth expressed by their use. Truth only arises given an “understanding” or “application” of the concepts expressed by those expressions, on a specific occasion of use.
Charles takes pains to guard against a misconception of these understandings or applications by which something determinate is said. There is no
right way of counting ways of understanding given words, or what they speak of … when these understandings are detached from some particular words that bear them, are considered as understandings for words to bear. (OS, 5; first emphases mine)
Such a misconception is tied to an interpretation of Frege’s notion of thought that Charles now rejects. According to the misconception, at some point
circumstances choose for us some truth-evaluable item which is itself immune in principle to admitting of different further understandings—[at which point], through appeal to circumstance, we arrive at the sort of invisible, intangible truth-bearer (what Frege called a ‘thought’) which, Frege held, was the only thing that could really make a determinate question of truth arise. (OS, 6; emphasis mine)
Charles goes on to note that he thinks there is another reading of Frege, “but one must work for it” (OS, 6). What is that work? What changed in Charles’s view of Frege so that Frege’s Gedanken are no longer taken to be the archetypal shadows of Unshadowed Thought (Reference Travis2000)?
I am going to approach an answer to this by thinking about how OS, free of the misconception just outlined, differs from a picture of context-sensitivity one could draw from David Kaplan (Reference Kaplan, Almog, Perry and Wettstein1989). Kaplan holds that contextual parameters serve, as it were, to build up an abstract entity, a proposition, a content, or a what is said. This entity is, or entails, truth conditions and, to vary Kaplan’s vivid imagery, is loaded into the trans-world spaceship, to be sent around possible worlds (or times) for evaluating whether the conditions there match the conditions for truth, or otherwise. I would like to highlight a distinction drawn by Kaplan in this picture, between contexts of utterance, in which a proposition is expressed, and circumstances of evaluation, with respect to which that proposition is determined as true or false. The former are, as it were, the labs where propositions are manufactured; the latter are the destinations to which propositions travel. Upon disembarking from TWA, a proposition asks, “Are things so here?” and the “here,” the circumstances of evaluation, to use Charles’s turn of phrase, disposes the question of truth proposed by that proposition.
The abstract entity built up in contexts of utterance Charles calls a shadow. The objection from OS to shadows is that they ignore the role of understanding or counting in the final step. No abstract entity, by itself, independent of how it is understood, or applied, by speakers or thinkers, on particular occasions of use, reaches, to use Charles’s term in the papers in OP, the world(s), or things, for that evaluation or comparison on which truth (or otherwise) turns. This reach essentially involves what they count as the world(s)’ or things’ instancing, or as I would like to put it, matching, the truth conditions.
The reading of Frege as committed to shadows (call it shadow Frege) takes Gedanken to be such Kaplan-style structured abstract entities. So, an initial idea about how to read Fregean Gedanken as non-shadows is this. A Gedanke, a way of making truth turn on a representation of things (being as they are) as some way for them to be, requires understanding or interpretation in order to reach, or to be instanced (or not?) by things, and thereby to have its question of truth answered. The thought that Sid imbibes, for instance, is instanced or not by things only gives an understanding or interpretation of what counts as imbibing on an occasion.
The misconception about OS bruited above amounts to what one might call domestication of understandings. This is the idea that features of the occasions of OS—occasions in which one expresses a thoughts by making an utterance, or just entertains a thought—determine certain understandings, such that, when it comes to comparing the thought with circumstances to evaluate its truth or falsity, these understandings step in and relieve the thinker or speaker in that occasion of any need, say, for understanding how the thought reaches to the circumstances. “Relieve” of course also admits of uses such as “federal agents relieved Pia of her pistols”; so here perhaps the idea might also be that if the thinker tries to pull a fast one by putting his understanding in place of the one fixed by occasion of expression/grasp, it would not lead to a lawful answer to the question of truth posed by the thought. The context has already chosen understandings; we may not interfere.
Such domesticated, farm-raised, understandings would not, one might think, be at bottom any different from other features of context that go to build up propositional shadows. Thus, equipping shadow Frege with domesticated understandings would not unshadow him. He would be, one could say, a faux unshadowed Frege. By the same token, if one were to outfit Kaplan with such farmed understandings, the resulting position would still be an epicycle of shadowed thought.
So far, I have linked the occasions of OS to contexts of utterance. Could domesticated understandings also be conceived of as parts of, or required adjuncts to, circumstances of evaluation? Perhaps like this: things being as they are, or being as they might be, do not, in themselves alone, answer or dispose questions of truth; they do so only given a domesticated understanding of how ways things might be apply to them.
This takes me to the reason why I have approached OS through a contrast to Kaplan. Kaplan is a temporalist, or at least sympathetic to such a position, so that, for him, times, along with possible worlds, are required for evaluations of what is said. Thus for temporalists, the truth and falsity of propositions expressed are relative to time and world.
There is no doubt that, when it comes to Gedanken, Frege is the very polar opposite of a temporalist. Here are some familiar expressions of his opposition. For example, in the latter of the two unpublished manuscripts entitled “Logik”:
It is of the essence of a thought to be non-temporal and non-spatial. [T]he thought is either true, in which case it is always, or better, timelessly, true, or it is false and in that case it is false without qualification. (Reference Frege1897, 135)Footnote 1
In the diary notes now known as “Einleitung in die Logik”:
It is nonsense to speak of cases in which a thought is true and cases in which it is false. The same thought cannot be true at one time, false at another. On the contrary, the cases people have in mind in speaking in this way always involve different thoughts, and the reason they believe the thought to be the same is that the form of words is the same; this form of words will then be an improper statement. (Reference Frege1906a, 186; last emphasis mine)Footnote 2
In “Der Gedanke”:
[A]re there not thoughts which are true today but false in half a year’s time? The thought, for example, that the tree there is covered with green leaves, will surely be false in half a year’s time. No, for it is not the same thought at all. The words ‘This tree is covered with green leaves’ are not sufficient by themselves to constitute the expression of thought, for the time of utterance is involved as well. Without the time-determination thus given[,] we have no thought at all. Only a statement with the time-determination filled out, a statement complete in every respect, expresses a thought. But this thought, if it is true, is true not only today or tomorrow but timelessly. (Frege, Reference Frege1918–1919, hereafter Ged, 76)Footnote 3
Since the truth and falsity of Gedanken are absolute, since there is no such thing as a Gedanke which is true or false only relative to person, place, time, or (possible) circumstances, there are no modes of truth founded on such relativization of truth. In particular, no Gedanke is necessarily true because true no matter how the world might be, or only possibly true because false in some alternative circumstances, as opposed to true, Punkt. I call this Fregean view amodalism about truth. It is opposed to various sorts of modalism about truth; Kaplan is, in my terminology, a temporal and circumstantial modalist.
Note that, in terms of the context of utterance versus circumstances of evaluation contrast, the passage from “Der Gedanke” just quoted may be read as claiming that something like the time at which an utterance is made is a feature of context of utterance that goes into the manufacture of the thought expressed, and that thought, once fully built, “complete in every respect,” has no need of TWA to get to propose its question of truth. Once built, it has, as it were, such Höhen over even the plurality of worlds that its question of truth reaches all their spatiotemporal corners without its having to travel anywhere (well, not being in space or time or the plenum of possible worlds, it cannot do any traveling anyway).
At this point, you may well ask, why is Frege an amodalist? Well, the reason is the crux of the matter for my understanding of Frege, and I am going to keep you in suspense a touch longer.
For the moment, I want to note that nothing, it seems to me, stands in the way of saddling a shadow version of Frege with amodalism, and so to disagree with shadow Kaplan. An amodalist shadow Frege holds both that Gedanken has their questions of truth answered without any need for understandings, and that these answers are absolute, not relative to thinker, place, time, or possible world.
Now, might one not, in addition to reinforcing Kaplan with domesticated understandings, take these understandings to belong to the truth evaluations of what are said? That is to say, the truth and falsity of propositions expressed are relative to time, world, and understanding. Call such a Kaplan faux unshadowed. It seems to me that the same disagreement between shadow Frege and Kaplan would be replayed between the faux unshadowed Frege and Kaplan. For the former, domesticated understandings count as ingredients or components or processes of manufacture of Gedanken expressed or grasped on occasions; once built, a Gedanke is as lordly as ever, needing no voyage for proposing its question of truth or getting it answered. For the latter, they count as what are required, perhaps at the end of the proposition’s flights, as a jet bridge or a flight of airstairs to be traversed in order to reach the possible ways for things to be, in order for said things to answer it question of truth. Faux unshadowed Kaplan simply adds understandings to the items relative to which truth and falsity are determined. He is an understanding modalist, while faux unshadowed Frege remains an amodalist.
So, the question for me is whether unshadowed Frege, with wild rather than farmed understandings required for answers to questions of truth posed by Gedanken, has to reject amodalism.
Here is my tentative case for a negative answer. To begin with, the wildness of understandings consists in the essential and irreplaceable role of thinkers’ (making use of their) sensibilities in bringing the questions of truth of representations to be answered by things. That is to say, without an application of understanding by thinkers on an occasion of expressing or grasping a thought, there is no truth or falsity to be acknowledged (anerkennt).
Next, let us consider some passages from “Der Gedanke” prominent in Charles’s reading of Frege:
I call a thought that by which truth can come into question at all. (Ged, 60)Footnote 4
But do we not see that the Sun has risen? and do we not then also see that this is true? That the Sun has risen is not an object emitting rays that reach my eyes; it is not a visible thing like the Sun itself. That the Sun has risen is recognized as true on the basis of sense-impressions. (Ged, 61; my emphasis)Footnote 5
If man could not think and could not take as the object of his thought something of which he was not the owner, he would have an inner world but no environment. But may this not be based on a mistake? … By the step with which I conquer an environment for myself I expose myself to the risk of error. (Ged, 73)Footnote 6
I read these passages as supporting the idea that, for Frege, Gedanken, that by which truth can come into question, are also essentially those by which we recognize (erkennen) how thing are, namely that they are as some Gedanke represent them as being. This is in part because of what I see as the ground of Frege’s insistence on the redundancy of predications of truth: to recognize a Gedanke as true (als wahr erkannt) is to recognize the obtaining, the being so, of what it represents. This recognition as true, together with acknowledgment as true (als wahr anerkannt) are two of Frege’s habitual characterizations of judgment. Moreover, this recognition as true is that by which we conquer (erobern) an environment. That is to say, judgment is that by which we attain knowledge of the world, and thought is, as it were, intrinsically made for judgment.
The upshot of this picture of Gedanken as intrinsically for judgment conceived of as opening up knowledge of the world (“unlocking the outside world,” “die Außenwelt aufschließt,” Ged, 75) is that anything short of enabling one to recognize how things are is not a Gedanke. A structured abstract entity such as a Kaplanian what is said, which is true or false only relative to times, is not something by which alone recognition as true is achievable, and so, is not a Gedanke. Neither is a faux unshadowed Kaplan proposition, true or false only relative to (domesticated) understandings. This is why a faux unshadowed Fregean Gedanke would in some way incorporate (farm) understandings: only with these understandings is recognition of truth, of how things are, achievable.
Now, finally, let us consider a fully unshadowed Frege. If a thought, a making truth turn on how things are, does not elicit an answer—true or false—without a thinker’s understanding, on an occasion of taking thought, of the way for things to be that it (the thought) represents things (being as they are) to be, then, independent of that understanding, that interpretation, it is no Gedanke. To put it in Kaplanian terms, wild understandings belong with contexts of utterance, not with circumstances of evaluation. Our understandings, on occasions of taking thought, form the thought we thereby take, rather than helping the world dispose the question of truth that an already formed thought proposes.
It seems to me Charles might agree. Here’s Charles speaking, I think in propria persona, albeit that of nearly three decades ago:
For any a and F, there are many thoughts, each thinkable on some occasion or other, all equally about a, and about its being F, each differing from the others in when things would be as they are according to it. (Travis, Reference Travis1994, 277; underlining mine)
A page later we read,
[I]f, in given surroundings, you call a leaf green, what you thus say is true just in case the way that leaf is counts, in those surroundings, as its being green. If, given the way the leaf is, you sometimes speak truth in calling it green, and sometimes do not, that can only be because in different surroundings different things would count as the leaf’s being green. A leaf may count as green on a particular understanding of what its being green would come to; circumstances may make one understanding or another the right one. (Travis, Reference Travis1994, 278)
The juxtaposition of these two passages leads me to this view. The leaf being the way it is remains the ultimate disposer. On the different occasions, we count different things as the leaf’s being green, where each such counting goes one of many distinct thoughts one would on those occasions be thinking.
What about now, nearly three decades later? Unshadowed Frege in FPB, it seems to me, accepts a perhaps more restricted version of this view: so far logic is concerned, there is no Gedanke except what is fixed by an understanding, and that is either true or false.
One of Frege’s objections to Korselt in “Über die Grundlagen der Geometrie, II” is:
The word ‘interpretation’ [‘Deutung’] is objectionable, for when properly expressed a thought leaves no room for interpretation. We have seen that ambiguity [Vieldeutigkeit] simply has to be rejected. (Reference Frege1906b, 384; like Charles, I quote Warren’s translation)Footnote 7
Commenting on this, Charles identifies two notions of interpretation that may be expressed by Frege’s “Deutung.” One is
Sid is presented as having ‘eaten the whole thing’. Must he have done so bones and all? Two distinguishable ways for things to be represented in representing someone to have ‘eaten the whole thing’ now need distinguishing. A Deutung in this first sense is now a set of features, or specification thereof, which draw the needed distinction.
Suppose someone points to a stuffed whale in a natural history museum and asks, ‘Is that a whale?’ What would it be for the right answer to be ‘Yes’? Again a Deutung in this first sense… may be called for. (FPB, 206)
Charles goes on to say:
A thought cannot admit of understandings, Deutungen [on this first notion]. If it admitted of a pair of understandings on one of which it would be true, on another false, it would not be, for logic’s purpose, a determinate question of truth.
… [I]n taking some thought-expression to be of some given thought, one accords that thought the status of last interpretation. But this need not mean that if the thought so identified is of things being such-and-such way, what it would be for something to be that way is immune to further interpretation of the first kind above. (FPB, 207; second emphasis mine)
Thus, at least as far as the purposes of (applying) logic is concerned, the OS of thought is the sensitivity or relativity of the thought entertained or grasped to occasion an understanding or interpretation suited to that occasion. But OS is not the relativity or sensitivity of the truth of one and the same thought from occasion to occasion. Given occasion and understanding, a thought is fixed, and it is either true or false, tertium non datur. That is all that is required, for the purposes of logic.
As far as logic is concerned, unshadowed Frege remains an amodalist. The path to modality via modalism remains closed to him, who shakes hands forever with Austin and the later Wittgenstein.
2. Das grösste Schwergewicht: der Höhen der Begriffe
Central to Charles’s interpretation of Frege’s is what he takes from the fourth of “17 Kernsätze zur Logik”:
A thought always contains something reaching beyond the particular case, by which this comes to consciousness as falling under something general (etwas Allgemein). (Reference Frege1884, 189)Footnote 8
Perhaps many readers of Frege take this “something reaching beyond the particular” to be a concept, or the sense thereof, which is a part a thought “contains” (on some decomposition). Charles reads the “something” as applying also to the thought itself, since thoughts, being 0-place concepts, “contain” generality as “a letter may contain thinly veiled contempt for its recipient” (PEF, 15).
However, when we turn to Charles’s account of why thought has this “generality,” we appear to find Old Nick himself lurking. To begin with, a thought is “a way for things to be,” “a way for truth to turn on how things are,” and “a particular way for things to matter to a sort of representing-as” (PEF, 6). But, now, a
way for things being as they are to matter to truth is, per se, fixed independent of things being as, in fact, they are. (Things might have been different while there was still that way for truth to matter.) Hence for truth to turn in that way on how things are cannot be for it to turn on everything as to how things in fact are. There is, then, what matters and what does not. For truth to turn on whether Sid smokes is, inter alia, for it not to count against truth that, for example, Pia smokes, or does not, or that Sid does, or does not, wear Bermuda shorts. So if things being as they are is a case of things being such that Sid smokes, such is one way for this to happen—one among indefinitely many ways.
Nor is this feature peculiar to things being such that Sid smokes. It is built into the very idea of a way for things to be; a feature of any such way. In the terminology used in these essays, a way for things to be (or for a thing to be) reaches to, or is instanced by, indefinitely many distinct (possible) cases. (PEF, 6; underlinings mine)
Here is a first pass at the line of thinking expressed here. Suppose Sid in fact smokes. And suppose in fact Pia does not smoke, and in fact Sid wears Bermuda shorts. Then the way things are is such that the thought that Sid smokes is true. But it is possible that alongside Sid’s smoking, Pia also smokes and Sid never wears Bermudas. Things would then be different (a different way?). But, still, the thought that Sid smokes remains true. It is also clear that things could be different in yet other ways—Sid might be nice to Benno, Pia might be a quaffer of Köstritzer Schwarz rather than a sipper of Legras et Haas, and so on—and yet the thought that Sid smokes remains true. There are then indefinitely many possible ways for things to be that would instance the thought that Sid smokes. Hence the (modal) generality of thought.
This first pass leaves me with some questions. First, why is the generality of thought a matter of possible instancing, rather than instancing at different actual places or times? Why is not the thought that Sid smokes general in virtue of his smoking in Kansas as well as Kenya, at home as well as at the department, or, in the morning as well as at night, in grad school and after being created emeritus? Second, why is any generality at all required for the representations-as that thoughts are? Is it inconceivable that Sid lit up exactly once, after hearing that he was denied tenure, but then, upon receiving Pia’s ultimatum—it is me or the demon weed—never again? Could there then be no thought, or no true thought that Sid smokes?
In FPB, we find generality connected with what Charles terms the “aloofness” of concepts, and aloofness characterized in modal terms:
A concept’s aloofness lies in its proprietary generality. Generality is a sine qua non for representing-as. A concept, so far, if not engaged in representing-as, is but one remove from this, lacking but representational intent. A concept is aloof from what falls under it. For non-singular concepts such aloofness typically manifests itself in the concept’s being what might have been fallen under by other than what does, or might be the one it is even if fallen under by nothing. It need not have been Sid who was the last to leave the pub. Others, and not Sid, might have tried (literally) to pull the rug out from under Benno. (FPB, 34; italics mine)
I am interested in two aspects of this view. First, how and why is the modal conception of aloofness connected with the generality that is essential for representing-as? In particular, can one exorcise, as my Frege did, modal notions and still retain a conception of concepts adequate for Charles’s representing-as? Second, is there indeed a connection between concepts and generality in Frege’s thinking? Exploring the second issue would take us too far afield, so I will just note that I would answer yes, on the ground that from Begriffsschrift on Frege conceived of contents of generality (not quantification, which is a different issue) in terms of what Dummett calls the “extraction” of functions or concepts from contents, and it is this extraction that underlies some of his central characterizations of concepts.
On the first issue, let me begin by noting that in FPB Charles takes Frege to have entertained three conceptions of concepts, only one of which, it seems to me, is tied to modality. This one is based on texts such as this passage from Frege’s letter to Marty:
You emphasize the division between the function of judgment and the matter judged. The distinction between individual and concept seems to me even more important. The relation of subordination of a concept under a concept is quite different from the falling of an individual under a concept. People, it appears, have followed too closely the linguistic schema of subject and predicate, and yet this contains two quite different logical relations. (Frege, Reference Frege1969b, 164)Footnote 9
Charles takes “falling under” to be “a relation obtaining where an object fits … a concept,” and Frege to be
thinking of a concept as attaching to, or simply of, a way for a thing to be, thus as the sort of thing a (one-place) proper predicative subthought, not the sort of thing a whole thought, or a relational subthought, would express. (FPB, 32)
Now, I take it that Charles is not identifying this conception of concept with predicative subthoughts, but rather what, if “redacted” from a specific predicative subthought, constitutes the specificity of that sub-thought. For example, a specific predicative subthought P 1 represents an individual as green. What distinguishes it from another predicative subthought P 2 which represents an individual as refined? Being green, of course, as opposed to being refined. Being green is a way for an individual to be; being refined is a different way for an individual to be. When we “redact” from P 1 being green and from P 2 being refined, we reach what all such subthoughts have or do in common, namely, represent an individual as being some way (for individuals to be). This common task of predicative subthoughts is a representing as being some way. One might call it, in terms I think Charles might find congenial, a vehicle of representational import. When the specific ways for an individual to be are loaded back into (“unredacting”) the vehicle, we get specific predicative representations. These ways are concepts of this first conception.
This first conception of concepts Charles also ties with Frege’s characterizing concepts as having “predicative nature (prädikative Natur)” (see, for example, “Über Begriff und Gegenstand” Frege Reference Frege1892, 197, 200):
[T]o have predicative nature is to predicate something of something, thus to engage in representing-as: to represent something as being something. On this line of thought a predicative subthought has predicative nature. So, too, does an improper predicative subthought, that is, a whole thought. A concept, on the redaction notion, does not, since it does not engage in representing-as. We could extend the term, so to speak, give concepts honorary predicative nature, on grounds that they are just what needs adding to the bare predicativeness of a predicative subthought to yield that whole, the subthought… (FPB, 40)
It seems to me that Charles is most sympathetic to this first Fregean conception of concepts, because of his taking predication to be representing-as, which goes with his view of Fregean thoughts as representations, and representations as the conceptual. I will call it the predicative nature conception of concepts.
Let me briefly mention the other two Fregean conceptions of concepts, both of which Charles views with some skepticism. The second conception is connected with Frege’s characterization of concepts, along with functions, as unsaturated (ungesättigt) and as in need of completion (ergänzungsbedürftig). Charles takes it that some sense can be made of this, in terms of the idea that there is no performing the tasks of the designative and predicative subthoughts into which a thought decomposes independently of one another. Each then, is by itself unsaturated and in need of being completed by the other. But on this idea unsaturation is not unique to the concepts that individuate predicative subthoughts, it belongs to designative sub-thoughts as well.
The third Fregean conception is that concepts are functions whose values are the two truth values. This Charles takes to be a mistake, perhaps even a “gratuitous blunder” (to use the words of Dummett, Reference Dummett1973, 184). Part of his reason for this, it seems to me, rests on a misreading of Frege’s notion of function as a certain sort of relation understood in something like set-theoretic terms as a class of ordered pairs. The closest, it seems to me, Frege comes to such an idea is the value-ranges of functions, not functions themselves. But I leave this disagreement over Frege interpretation aside in the following.
Having now, I hope, cleared the ground a bit, let us turn to how and why the generality of representing-as of concepts is characterized modally.
One route to this view seems to be an interpretation of Frege’s insistence on a fundamental distinction between concept and object. Charles draws on a discussion in “Logik in der Mathematik” of the distinction between the subsumption of objects under concepts and the subordination of a concept to another:
In the sentence ‘Cato is mortal’ I have a subsumption, in the sentence ‘All men are mortal’ a subordination. A concept is spoken about here, not an individual. We also must not think that the sense of the sentence ‘Cato is mortal’ is contained in that of the sentence ‘All men are mortal’, so that by uttering the latter sentence I should at the same time have expressed the thought contained in the former sentence. (Frege, Reference Frege1914, 230–231)Footnote 10
Charles takes Frege’s point to rest on the patent invalidity of inferring, from “all humans are mortal,” “Cato is mortal.” This invalidity shows that a concept expression such as “human” is not “a polysemous name, naming indifferently all and only the humans” (FPB, 36); if “human” were such a name, it would already denote Cato, and so the inference would be valid. The moral is that a concept stands “to what it fits, or applies to, in a way fundamentally different from denotation” (FPB, 33). This moral is further spelled out as follows:
An item need not fall under a concept for it to be represented as so doing. So things must be if there is to be truth and falsehood. Whereas an item can be the one so represented only if so denoted in the thought which does so. A concept must be aloof enough from its extension so to differ from denoting. (FPB, 33)
Does this passage express an argument? Perhaps it is this line of reasoning:
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• Some representations are false.
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• Suppose no thought represents an object as falling under a concept even though it does not so fall.
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• Then there are no false representations.
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• Hence some thoughts represent objects which do not fall under concepts as falling under those concepts.
The conclusion of this line of thinking, that some concepts which do not apply to certain objects are represented in thoughts as applying to those objects, would then be the aloofness, the Höhen, of concepts over objects. Let us call this argument and the passage from which I drew it aloofness from falsity.
Charles continues with a further elaboration of aloofness:
What [aloofness] comes to is this: a concept is identified as the one it is … by what it would be for something to fall under it (to be what it is a concept of being)—by its proprietary way of separating out what would so count from what would not; of generalizing over and beyond any given case of a thing … being as it is. (FPB, 33)
Is this further elaboration a continuation of the aloofness from falsity argument? Prima facie, this elaboration advances some three, possibly equivalent characterizations of aloofness in terms of how “a concept is identified as the one it is”:
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• by what it would be for something to fall under it (to be what it is a concept of being),
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• by its proprietary way of separating out what would so count from what would not, and
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• [by its way] of generalizing over and beyond any given case of a thing being as it is.
Perhaps there is an argument to the effect that unless a concept “is identified as the one it is” in one of these ways, there would be no false representation.
How would this work? Maybe like this. Suppose a concept is “identified” by what does, rather than what would, fall under it. Here, one might think, possibility enters the stage: the supposition might be understood as taking the identity of a concept to lie in what is the case rather than what might be the case. It follows then that there is no representing an object as falling under that concept unless it does fall under it, and so there is no false representation.
I do not, however, see how the last step is supposed to work. Here is one way of approaching my puzzlement. Suppose concepts are (actual) extensions, that is, something like sets of objects that we think of as falling under them. So the concept of being a prime number is the set of all primes. What stands in the way of representing, for example, 26, as a member of this set? Perhaps someone who knows the condition for membership in this concept might work out that 26 fails this condition and so is not a member of this set. Perhaps such a person would not represent 26 as a member. But does this mean that there is no such thing as representing 26 as a member of the set of primes?
Perhaps there is a path to possibility from the third characterization of aloofness is in terms of “generalizing over and beyond any given case.” Another characterization of aloofness which I quoted earlier in linking aloofness with generality is this: “the concept’s being what might have been fallen under by other than what does.” This suggests that “beyond any given case” is something like “beyond any actual case,” or “applicability to possible non-actual cases.” But I do not see a sure path to possibility. For, here is a way of characterizing a notion of the generality of concepts non-modally: in general, if a falls under a concept P, the assumption that another object b falls under P does not contradict the laws of logic. Alternatively, (∃P)(∃a)(∃b)(a ̸= b &Pa &Pb) is logically consistent. What is missing, if this is what the generality of concepts comes to?
The foregoing applies to non-singular concepts. What are singular concepts? The examples Charles provides are concepts of being identical with some specific entity, for example, Frege, which is the concept of “being that very one Frege” (FPB, 34). Obviously(?) only Frege falls under this concept; a “concept fallen under by someone else would eo ipso not be that one: it would not be of being Frege” (FPB, 34). Charles, it seems to me, takes this truism(?) to go against the characterization of aloofness and generality for non-singular concepts, they “might have been fallen under by other than what does.” For this reason, Charles holds
that the most general manifestation of that phenomenon, aloofness, its universal mark, does not lie in the relation falling under. Falling-under is a relation between an object and a concept. With singular concepts in view, aloofness manifests its most general form in terms of a different relation. (FPB, 34)
The relation that does get at the heart of aloofness is instancing, and it is explained in terms of the notion of residue. A predicative nature concept is a way for things or a thing to be. It is “an articulate of things being as they are/a thing as it is; an articulation which leaves a residue” (FPB, 34). Charles’s example helps to clarify what this might mean:
For something to be as the object on Sid’s plate is, inter alia, for it to be a sandwich. Such is one thing which would so count. After Sid adds the aioli and the jalapeños, what is then on his plate is another thing which would so count. That object on Pia’s plate—the écrivesses [sic] with cress—is another thing which would so count, and so on. (FPB, 34; third italics in text)
All these objects, with different features and constitutions, instance “what the concept sandwich is a concept of” (FPB, 34). What is the residue? I am not sure, but I would surmise that, whatever the residue is, the undomesticated understandings of OS traverse it, reaching from the concept to the instancings of the concept. Now, Charles says that instancing “contrasts with falling-under” (FPB, 35). Does this mean that all these objects on plates do not fall under the concept sandwich? I rather doubt it. I surmise, rather, that they all do fall under sandwich, but they do so only courtesy of an understanding by which they count as sandwiches, and so instance sandwich. If I am right, then instancing is in some sense prior to falling-under, and this explains why the Höhen of singular concepts is not manifest through falling-under. Here is a case devised by Charles for distinguishing between falling-under and instancing a singular concept, the concept of being that very one Sid:
Suppose Sid changes his ways—or, that is, does so if the result of the changes is still Sid. So we now find an object nattily attired, sipping from a flute of Billecart-Salmon, exchanging aperçus with the other pseuds at the vernissage of the latest dernier cri. Suppose, further, that this now-exquisitely sensitive personage is actually polite to Benno. Could this be Sid? Would anything so changed be him? Perhaps. But the answer depends on what it would be for an object to be Sid; when an object’s being as it is would be such a case. (FPB, 35)
The question of whether the now-exquisitely sensitive personage, call it Schmid, counts as Sid is open. Open, that is, to being settled differently by different understandings of, as it were, Sidicity. A settling fixes whether Schmid (a residue?) instances being Sid. If it does, then of course it falls under being that very one Sid. But there is an alternative settling, on which Schmid does not count as being Sid, fails to instance being Sid. Schmid then does not fall under that singular concept.
Now, was not a, if not the point of instancing the re-insinuation of possibility into the conceptual? That is to say, even though no singular concept “might have been fallen under by other than what does,” singular concepts might have been instanced by other than what does instance them. How would this work in the case of being that very one Sid? Is it that the beBermudaed individual who staggers out of der alte Schnorrer after having poured his fifth liter of Schlenkerla Helles on Benno’s head, call it alte-Sid, is other than Schmid, but both instance being that very one Sid, because each counts, on some understanding, as being that very one Sid?
I have no interest in domesticating understandings (though it may turn out that I have already unwittingly domesticated in some way distinct from that of Section 1). But I wonder about the “might have” in the foregoing: alte-Sid does(?) instance, while Schmid might have instanced, being that very one Sid. “Might have,” I want to suggest, here means the possibility of describing an occasion, a “when” of Austin’s “what we should say when” (Reference Austin1956, 7), such that those Austin call “we,” with our parochial sensibilities, discern a point to the application of being that very one Sid, and so “should say,” as Austin puts it, of, for example, Schmid, that it is that very same one, Sid. I will not here attempt such a description, leaving it to Charles, who is, after all, the master of “Travis cases” (Collins & Dobler, Reference Collins, Dobler, Collins and Dobler2018, 2, passim), should he be so moved. I will, instead, put in a word for Frege the amodalist. First of all, he would rephrase the alternative instancings as something like conditionals: if … (here goes a description of an occasion, an Austinian “when”) …, then such-and-such is (“we should say”) (that very one,) Sid. Second, let us go back to Frege’s account of calling a Satz possible which I mentioned at the outset. I said that in some cases, according to Frege, someone who does so is hinting that she is not judging at all. Well, I left out what Frege goes on to say about these cases: the speaker also hints that she knows no laws contradicting what she calls possible. So, according to Fregean amodalism, one who says that there might be an understanding on which someone other than (alte-)Sid instances being Sid is giving a Wink that no law (of logic, of semantics, of implicature, or what have you) rules out the existence of descriptions of Travis cases such that conditionals with such descriptions in the antecedent and an ascription of being Sid in the consequent are true. I do not see that an amodalist unshadowed Frege has any reasons to object to what is thus hinted. Nor do I see that Austin and the later Wittgenstein would have any reason to reject it, and stop shaking hands forever with this Frege.
Sanford Shieh is Professor of Philosophy at Wesleyan University. He works on the philosophy of logic and metaphysics through the philosophical history of the analytic tradition. He recently published Necessity Lost (2019), which won the 2020 Book Prize of Journal of the History of Philosophy.
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